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Home , Meteoroid, Micrometeoroid

A&A 551, A27 (2013) DOI: 10.1051/0004-6361/201220541 & c ESO 2013 Astrophysics

Micrometeoroids flux on the

G. Cremonese1, P. Borin1, A. Lucchetti2, F. Marzari2, and M. Bruno3

1 INAF-Astronomical Observatory of Padova, Vicolo dell’Osservatorio 5, 35131 Padova, Italy e-mail: [patrizia.borin;gabriele.cremonese]@oapd.inaf.it 2 Department of Physics and Astronomy, via Marzolo 8, 35131 Padova, Italy e-mail: [email protected] 3 Department of Mineralogical and Petrological Science, via Valperga Caluso 35, 10125 Torino, Italy e-mail: [email protected] Received 11 October 2012 / Accepted 24 December 2012

ABSTRACT

Context. The Moon has a tenuous exosphere consisting of atoms that are ejected from the surface by energetic processes, including micrometeoritic impacts, photon-stimulated desorption by UV radiation, and ion sputtering. Aims. We calculate the vapor and neutral Na production rates on the Moon caused by impacts of in the radius range of 5−100 μm. We considered a previously published dynamical model to compute the flux of meteoroids at the heliocentric distance of the Moon. Methods. The orbital evolution of dust particles of different sizes is computed with an N-body numerical code. It includes the effects of Poynting-Robertson drag, solar wind drag, and planetary perturbations. The vapor production rate and the number of neutral atoms released in the exosphere of the Moon are computed with a well-established formulation. Results. The result shows that the neutral Na production rate computed following our model is higher than previous estimates. This difference can be due to the dynamical evolution model that we used to compute the flux and also to the mean velocity, which is 15.3 km s−1 instead of 12.75 km s−1 as reported in literature. Conclusions. Until now, the micrometeoritic impacts have been considered a negligible source for the release of neutral atoms into the exosphere compared to other mechanisms, but according to our calculations, the contribution may be 8% of the photo- stimulated desorption at the subsolar point, becoming similar in the and dusk regions and dominant on the night side. Key words. methods: statistical – , meteors, meteoroids – Moon

1. Introduction was proposed as the dominant source mechanism of this ele- ment in the lunar exosphere (Sprague et al. 1992). Morgan et al. The Moon has an extended and tenuous exosphere that contains (1988) suggested impact vaporization due to sodium and potassium. The presence of these two elements in as a source for the steady-state exosphere of the Moon. This the lunar was first detected from optical ground- theory was validated during the Leonid event in based observations made by Potter & Morgan (1988)andwas November 1998 (Smith et al. 1999). The ion sputtering is also confirmed by Tyler et al. (1988). believed to be a sodium source at the Moon (Potter & Norgan Different mechanisms and source processes have been pro- 1988), but there is no verified evidence about this contribution. posed as possible sources of the sodium and potassium (Hunten The present work reports the neutral Na production rate on & Sprague 1997; Killen & IP 1999), including sputtering by the the Moon caused by impacts of micrometeoroids that originate solar wind, photon-stimulated desorption (Madey et al. 1998; from the Main Belt . To estimate the total contribution of Mendillo et al. 1999; Yakshinskiy & Madey 2004), thermal des- mass to the exosphere by the impacts, we have orption (Yakshinskiy & Madey 2000), and micrometeoritic im- to take into account the impactors flux on the Moon, the surface pacts (Cintala 1992; Mendillo & Baumgardner 1995; Cremonese composition, and the interaction with the exosphere. We have & Verani 1997; Verani et al. 1998; Smith et al. 1999). considered the dynamical model of the micrometeoroids flux at The loss processes of atoms from the surface are due to Jeans the heliocentric distance of the Moon (Borin et al. 2009). escape, photo-ionization with subsequent plasma pick-up by the solar wind, dispersal of neutral gases by solar radiation pressure, and recombination with on the surface. The continuous 2. Dynamical evolution model refill of the layer on the Moon comes from meteorites. Repetitive impacts shake the surface by means of fragmentation To estimate the meteoritic flux at the Moon we used the dy- and emersion of new material so there is a continuous turnover namical evolution model of dust particles of Marzari & Vanzani that supplies the surface with fresh material (Killen et al. 2007; (1994), which numerically integrates a (N+1)+M body problem Morgan et al. 1988). ( + N + M body with negligible mass) with the high- The sodium distribution around the Moon, observed by mean precision integrator RA15 version of the RADAU integrator by wide-angle imaging (Flynn & Mendillo 1993) and the varia- Everarth (1985). Radiation, solar wind pressure, and Poynting- tion in the sodium emission with the altitude (Potter et al. 2000) Robertson drag are included as perturbative forces together with seems caused by the photon-stimulated desorption (PSD), which the gravitational attractions of all planets in the . Article published by EDP Sciences A27, page 1 of 4 A&A 551, A27 (2013)

We computed the orbital evolution of the dust grains until Planetary coordinate systems are defined relative to their all particles move well inside the of -Moon system. mean axis of rotation. The direction of the north pole is spec- To estimate the flux of impacting grains we used a statistical ified by the value of its right ascension α0 and declination δ0, approach since the number of computed impacts is negligible. whereas the location of the prime meridian is specified by the Each time a dust grain falls within ten times the influence sphere angle that is measured along the ’s equator in an easterly of the Earth-Moon system, we recorded the minimum approach direction with respect to the planet north pole from the node Q ◦ distance and the grain–planet relative velocity. At the end of the (located at right ascension 90 + α0) at the planet’s equator on run we have a list of close encounters we can statistically ana- the standard equator to the point B where the prime meridian lyze. We divided the encounters into bins of radial distance from crosses the planet’s equator. The right ascension of the point Q ◦ the planet center and performed a leasts-squares fit to the data is 90 + α0 and the inclination of the planet’s equator to the stan- 2 ◦ with a parabola function as P0R . The leasts-squares fit,√ per- dard equator is 90 − δ0. Because the prime meridian is assumed formed assuming a standard deviation for each data bin of Ni to rotate uniformly with the planet, W accordingly varies lin- (where Ni is the number of close encounters in each bin), allows early with time. The rotation matrix C from inertial barycentric one to compute the parameter P0 (Marzari et al. 1996). Using for to body fixed frame is given by R the radius of Earth, we obtain the fractional number of impacts C (α + ◦, ◦ − δ, w) = R (W) R ( ◦ − δ) R (α + ◦) , on the surface of the planet nM. To calibrate our results we used 90 90 z x 90 z 90 (3) the flux curves obtained by Cremonese et al. (2012) who revised where the pole orientation angles α, δ and the direction of the the dust particle flux impacting the Earth. They simulated the prime meridian W are specified as linear function of time t mea- impact craters measured on the Long Duration Exposure Facility sured from some epoch t (Seidelmann et al. 2002), so with the shock physics code iSALE. p0 ⎧  ⎪ α = α + α˙ t − t ⎨⎪ 0  p0 2.1. Flux on the Moon δ = δ + δ˙ − ⎪ 0 t tp0 (4) ⎩⎪ To extrapolate the terrestrial flux to the Moon, we have taken into W = W0 + W˙ t − tp0 . account the different gravitational focusing factor, considering that the micrometeoroid flux on the Moon can be computed from Usually,α ˙ and δ˙ are measured in degrees per Julian Century that on the Earth as (Vanzani et al. 1997) so the term t − tp0 in the first two equation of (4)represents v2 an interval in Julian Century of 36 525 day from the standard F = F M , (1) epoch. In contrast the term t − t in Eq. (4) involving W repre- M E v2 p0 E sents a time interval measured in days from the standard epoch. The expressions for α and δ in the Moon system are taken from where FM is the flux at the Moon, FE is the flux at the Earth, v2 = . −1 v2 = . −1 Seidelmann et al. (2002). M 15 3kms and E 18 6kms are the average impact velocities on the Moon and on the Earth derived from the dynam- So we can obtain ⎧ ⎫ ⎧ ⎫ ical model (Borin et al. 2009), neglecting atmospheric deceler- ⎪ X ⎪ ⎪ x ⎪ ff ⎪ ⎪ ⎪ ⎪ ation. The di erence between the two values is mainly due to ⎨⎪ ⎬⎪ ⎨⎪ ⎬⎪ the diverse . Using the velocity values previously ⎪ Y ⎪ = C(α + 90◦, 90◦ − δ, w) ⎪ y ⎪ , (5) ⎪ ⎪ ⎪ ⎪ reported, we obtain a flux on the Moon that is 0.6766 times that ⎩⎪ ⎭⎪ ⎩⎪ ⎭⎪ given on the Earth. Z z Another aspect to be considered for the flux arriving on the where (X, Y, Z) are the particle coordinates in the Moon refer- lunar surface is the possible shielding due to the Earth. To cal- ence system considering the rotation of the satellite, whereas culate the shielding factor we assumed as key parameter the dis- (x, y, z) are the particle coordinates at the minimum distance tance between the two bodies. We computed the solid angle of from the satellite in the inertial reference system. Earth view from the Moon, on two orbit arcs centered on the perigee and the apogee, according to the following equation: α 4. Vapor production Ω=2π 1 − cos , (2) 2 The volume of target material vaporized by a spherical particle of mass m and impacting velocity v, can be estimated using the RE where α = 2arctan , with RE = Rmean + Ratmosphere = dEM relation given by Cintala (1992) 6378.134 + 650 000 km and dEM is the Moon-Earth distance. The ratio between Ω and the angle subtended from the area m 2 Vvap(v, m) = (c + dv + ev ), (6) affected by the impacting particles, in a specific range of incli- p nations, is 10−3, which is negligible.  = . g where m and p 2 5 cm3 are the mass and density of the mete- oroid that impacts the surface, c is a constant, d and e are given 3. Rotation from an inertial barycentric frame in km−1 s and km−2 s2 and depend on target temperature and pro- to a body-fixed frame jectile composition (Cintala 1992). Assuming that the vapor composition is determined by the To analyze asymmetries in the flux on the Moon we have to com- target composition, the production rate (atoms cm−2 s−1)ofneu- pute latitude and longitude of particles that impact the satellite. tral atoms S Na, is calculated by the relation (Morgan & Killen Computating the coordinates of dust particles that impact the 1997) Moon surface is performed in the body-fixed reference frame of the extended body. This necessitates introducing the rotation fNa S Na = Mvap NA, (7) matrix from an inertial to a body-fixed reference frame. pNa A27, page 2 of 4 G. Cremonese et al.: Micrometeoroids flux on the Moon

−2 −1 where Mvap is the vapor production rate (g cm s ), pNa is the atomic weight of the atom, NA is the Avogadro number and fNa = 0.00356 is the mass fraction of the neutral atom in the surface as used in previous works (Bruno et al. 2006, 2007). It is possible to calculate Mvap by integrating the equation vmax mmax Mvap = t φ(v, m)Vvap(v, m)dvdm, (8) vmin mmin  = . g φ v, ff where t 1 8 cm3 is the target density, ( m) is the di erential number of impacts as a function of the velocity and −1 −1 radius, vmin = 0kms , vmax = 80 km s , mmin = 1.309 × −9 −5 10 g, mmax = 1.047 × 10 g. Using the same formalism as Cintala (1992), the differential flux can be written as

φ(v, m) = f (v) · h(m), (9) Fig. 1. Micrometeoritic flux on the Moon in the radius range of 5−100 μm in the four different sectors of the as a function where f (v) is the velocity distribution of dust particles (s/km) of the latitude. and h(m) is the mass distribution function of the impacting parti- − − − cles (g 1 cm 2 s 1). The velocity distribution function is derived Table 1. Vapor production rate, number of Na atoms released, and for the Moon from numerical simulations (Borin et al. 2009)and micrometeoritic flux for each sector. is given by the following equation    Orbit sector M g S atoms Flux g v2 vap cm2 s Na cm2 s cm2 s 2 − 3 2 f (v) = a 2 v exp − · b, (10) − ◦ . × −16 . × 4 . × −16 B π 2a 150 210 3 051 10 2 845 10 1 155 10 330−30◦ 2.727 × 10−16 2.543 × 104 1.032 × 10−16 − ◦ . × −16 . × 4 . × −16 where a = 91.25 and b = 2.457 × 104 are constants. The derived 60 120 2 775 10 2 588 10 1 051 10 − ◦ . × −16 . × 4 . × −16 mass distribution function is given by 240 300 3 002 10 2 800 10 1 137 10 hB(m) = (k ± Δk) · hC(m), (11) Table 2. Mean values of vapor production rate, number of Na atoms released, and micrometeoritic flux over the entire lunar orbit. where hB(m) is a fit of the data obtained by means of simulations, hC(m) is the mass distribution function given by Cintala (1992)    g atoms g and k is an opportune constant, with the associate error, which Mvap cm2 s S Na cm2 s Flux cm2 s tunes the Cintala mass distribution function to the simulations 1.767 × 10−15 1.648 × 105 6.688 × 10−16 data (Borin et al. 2009). Table 3. Number of Na atoms obtained by different authors. 5. Results  atoms To compute the vapor production rate, the flux, and the num- Reference article S Na cm2 s ber of neutral atoms released into the exosphere, we took into Ip (1991) 1.8−3.7 × 104 account four different sections of the lunar orbit: the apogee . × 3 ◦ ◦ ◦ ◦ ◦ ◦ Cintala (1992)63 10 (330−30 ), the perigee (150−210 ), 60 −120 , and 240 −300 . Smyth & Marconi (1995) 2−3 × 104 Figure 1 shows the asteroidal micrometeoritic flux on the Moon Flynn & Mendillo (1995) 9.2 × 104 as a function of the latitude for each sector. The plots were ob- Morgan & Killen (1997)3× 104 tained assuming impacting dust particles in the radius range of Wilson et al. (1999) 1.8 × 104 5−100 μm. There is clear evidence of the vapor production rate Bruno et al. (2006)3−4.9 × 104 peak in the equatorial region. Table 1 shows the values of the Lee et al. (2011) 1.8 × 104 vapor production rate, the number of Na atoms released into the exosphere, and the asteroidal micrometeoritic flux for each sec- tor. Table 2 reports the value of the number of neutral sodium Our Na production rate is up to a factor 5.5 higher than the atoms calculated over the entire lunar orbit, which is higher than estimate reported by Bruno et al. (2007),whousedthesame the values obtained by other authors (Table 3). Cintala equations, but without applying a specific dynamical It is interesting to note that the higher Na production rate, ac- model. cording to our results, may be closer to the fit of the observations The most recent calibration of the terrestrial flux, that we discussed by Sprague et al. (2012), where the authors showed a have applied (Cremonese et al. 2012), contributed to reduce the ff difference of one order of magnitude between the Na production di erence with other authors to a factor 5, always assuming dust rate caused by PSD and by impacts. particles released by . The difference in Na production rate caused by impacts is mostly due to the dynamical model that we used to obtain the 6. Conclusions flux and also to the mean velocities (15.3 km s−1 and 18.6 km s−1 for the Moon and the Earth) which are different from other We reported the neutral Na production rate on the Moon caused previously assumed values (e.g. Cintala used 12.75 km s−1 for by impacts of micrometeoroids that originate from Main Belt the Moon). asteroids. To estimate the total contribution of mass to the

A27, page 3 of 4 A&A 551, A27 (2013) exosphere by the micrometeoritic impacts, we took into account Cintala, M. J. 1992, J. Geophys. Res., 97, 947 the flux on the Moon, the surface composition, and the inter- Cremonese, G., & Verani, S. 1997, Adv. Space Res., 19, 1561 action with the exosphere. We considered the dynamical evolu- Cremonese, G., Bruno, M., Mangano, V., et al. 2005, Icarus, 177, 122 Cremonese, G., Borin, P., Martellato, E., et al. 2012, ApJ, 749, L40 tion model of the micrometeoroids flux at the heliocentric dis- Everhart, E. 1985, Astrophys. Space Sci. Lib., 115, 185 tance of the Moon (Borin et al. 2009), calibrated according to Flynn, B., & Mendillo, M. 1993, Science, 261, 184 Cremonese et al. (2012). We obtained the number of Na atoms Grün, E., Zook, H. A., Fechtig, H., et al. 1985, Icarus, 62, 244 as 1.648 × 105 atoms/cm2 s, which is higher than the value of Hunten, D. M., & Sprague, A. L. 1997, Adv. Space Res., 19, 1551 Killen, R. M., & Ip, W-H. 1999, Rev. Geophys., 37, 361 other authors, suggesting that the impact process due to microm- Killen, R. M., Cremonese, G., Lammer, H., et al. 2007, Space Sci. Rev., 132, 433 eteoroids can play a very important role in the contribution of Madey, T. E., Yakshinskiy, B. V., Ageev, V. N., et al. 1998, J. Geophys. Res., neutral atoms to the exosphere. Previous estimates assumed that 103, 5873 the micrometeoritic impacts are a negligible source, about 1%, Marzari, F., & Vanzani, V. 1994, A&A, 283, 275 compared to the value of 2 × 106 atoms/cm2 s produced by PSD Marzari, F., Scholl, H., Farinella, P., et al. 1996, Icarus, 119, 192 Mendillo, M., & Baumgardner, J. 1995, , 377, 404 (Morgan et al. 1989; Sarantos et al. 2010). Our new evaluation Mendillo, M., Baumgardner, J., Wilson, J., et al. 1999, Icarus, 137, 13 of the impact vaporization mechanism raises the contribution to Morgan, T. H., & Killen, R. M. 1997, Space Sci., 45, 81 the 8% of PSD at the subsolar point. Assuming that the PSD Morgan, T. H., Zook, H. A., & Potter, A. E, 1988, Icarus, 75, 156 rate decreases as the cosine of the solar zenith angle, while our Morgan, T. H., Zook, H. A., & Potter, A. E. 1989, Production of sodium vapor from exposed regolith in the inner Solar System, Proc. 19th Lunar Sci. Conf., dynamical model shows no asymmetry in longitude for the mi- 297 crometeoroids flux, the contribution of the impact vaporization Potter, E. E., & Morgan, T. H. 1988, Science, 241, 675 becomes similar nearby the dawn and dusk regions and domi- Potter, A. E., Killen, R. M., & Morgan, T. H. 2000, J. Geophys. Res., 105, 15073 nant in the night side. Sarantos, M., Killen, R. M., Surjalal Sharma, A., et al. 2010, Icarus, 205, 364 Our result shows that impact vaporization is also very similar Seidelmann, P. K., Abalakin, V. K., Bursa, M., et al. 2002, Celest. Mech. Dyn. Astron., 82, 83 to the ion sputtering mechanism at the subsolar point, that is Smith, S. M., Wilson, J. K., Baumgardner, J., et al. 1999, Geophys. Res. Lett., 4 2 2.65 × 10 atoms/cm s (Sarantos et al. 2010), and is dominant 26, 1649 for other longitudes. Sprague, A. L., Kozlowski, R. W. H., Hunten, D. M, et al. 1992, Icarus, 96, 27 Sprague, A. L., Sarantos, M., Hunten, D. M, et al. 2012, Can. J. Phys., 90, 1 Tyler, A. L., Hunten, D. M., Kozlowski, R. W. H., et al. 1988, Geophys. Res. References Lett., 15, 1141 Vanzani, V., Marzari, F., Dotto, E., et al. 1997, Lunar and Borin, P., Cremonese, G., Marzari, F., et al. 2009, A&A, 503, 259 XXVIII Bruno, M., Cremonese, G., Marchi, S., et al. 2006, MNRAS, 367, 1067 Verani, S., Barbieri, C., Benn, C., et al. 1998, Planet Space Sci., 46, 1003 Bruno, M., Cremonese, G., & Marchi, S. 2007, Planet. Space Sci., 55, 1494 Yakshinskiy, B. V., & Madey, T. E. 2000, Surf. Sci., 451, 160 Burns, J. A., Lamy, P. L., & Soter, S. 1979, Icarus, 40, 1 Yakshinskiy, B. V., & Madey, T. E. 2004, Icarus, 168, 53

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